Question: Simplify the following expression: $ a = \dfrac{-4}{9} - \dfrac{7}{-6k - 10} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-6k - 10}{-6k - 10}$ $ \dfrac{-4}{9} \times \dfrac{-6k - 10}{-6k - 10} = \dfrac{24k + 40}{-54k - 90} $ Multiply the second expression by $\dfrac{9}{9}$ $ \dfrac{7}{-6k - 10} \times \dfrac{9}{9} = \dfrac{63}{-54k - 90} $ Therefore $ a = \dfrac{24k + 40}{-54k - 90} - \dfrac{63}{-54k - 90} $ Now the expressions have the same denominator we can simply subtract the numerators: $a = \dfrac{24k + 40 - 63 }{-54k - 90} $ Distribute the negative sign: $a = \dfrac{24k + 40 - 63}{-54k - 90}$ $a = \dfrac{24k - 23}{-54k - 90}$ Simplify the expression by dividing the numerator and denominator by -1: $a = \dfrac{-24k + 23}{54k + 90}$